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Bhattacharyya angle

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In statistics, Bhattacharyya angle, also called statistical angle, is a measure of distance between two probability measures defined on a finite probability space. It is defined as

where pi, qi are the probabilities assigned to the point i, for i = 1, ..., n, and

is the Bhattacharya coefficient.[1]

The Bhattacharya distance is the geodesic distance in the orthant of the sphere obtained by projecting the probability simplex on the sphere by the transformation .

This distance is compatible with Fisher metric. It is also related to Bures distance and fidelity between quantum states as for two diagonal states one has

See also

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References

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  1. ^ Bhattacharya, Anil Kumar (1943). "On a measure of divergence between two statistical populations defined by their probability distributions". Bulletin of the Calcutta Mathematical Society. 35: 99–109.